The transmit distortion is denoted by \(\textbf {z}_t\) , whose elements are independent and follow \( \mathcal {CN} (0, k_u p_k)\) , where \(k_u\)  measures the severity of the residual impairments at the transmitter. The receive distortion is denoted by \(\textbf {z}_r\) , and follows \( \mathcal {CN} \big (0,k_b\sum _{i=1}^{K}\widetilde{diag}\lbrace \widetilde{\textbf {y}}_i\widetilde{\textbf {y}}_i^H\rbrace \big )\) , where \(k_b \)  measures the severity of the residual impairments at the receiver, \(\widetilde{\textbf {y}}_i=\textbf {g}_i(\sqrt{p_i}x_i + z_{t,i})\)  and \(z_{t,i}\)  is the \(i\) -th element of \(\textbf {z}_{t}\) . Here, \(\textbf {z}_t\)  models the joint effects of the non-linearities in power amplifier and digital-to-analog converters, the power amplifier noise and oscillator phase noise. \(\textbf {z}_r\)  models the joint effects of the non-linearities in analog-to-digital converters and automatic gain control (AGC), the AGC noise and the oscillator phase noise [1]}.
